In such flow machines, the hot fluid, e.g. hot combustion gases, contained in the first space give rise to high temperatures in various components and regions of components. Consequently, these components require to be cooled efficiently in order to be able to guarantee reliability and a long life time of the flow machine.
An example of a component that requires such efficient cooling is the wall of a guide vane platform in a gas turbine engine, especially a wall of the guide vane platform of the high pressure guide vane stage, where the hot combustion gases have a very high temperature.
A known cooling arrangement for such a platform wall is defined above and disclosed in FIG. 1 attached hereto. FIG. 1 shows a first space 1 through which the hot combustion gases may flow. The first space 1 is delimited by wall 2 of the platform 3 to which the aerofoil 4 of the guide vane is attached. The wall 2 has a first wall surface 2a facing the first space 1 and a second wall surface 2b turned away from the first space 1. Cooling means is provided for cooling rear region of the wall 2 by supplying a relatively cool fluid onto the second wall surface 2b. A supply chamber 6 contains the relatively cool fluid. A cavity 7 is arranged immediately adjacent to the second wall surface 2b and at least one duct 8 extends from the supply chamber 6 to the cavity 7 and conveys the relatively cool fluid from the supply chamber 6 to the cavity 7. A rotor shroud segment 9 presents a deflection surface 9a facing the cavity. The deflection surface 9a re-directs the cool fluid from the duct 8 towards the second wall surface 2b. 
As can be seen in FIG. 1, the deflection surface 9a extends along a straight line in an axial plane. The deflection surface 9a is curved in a circumferential direction perpendicular to the axial plane. It has now been recognised that the cooling arrangement does not provide any significant heat transfer to the rear region of the wall 2, which means that the cooling of the rear region of the wall 2 will be insufficient or that a quantity of cool fluid to be supplied will be unacceptably high.